98-710 Mohamed Sami ElBialy

Sub-stable and weak-stable manifolds associated with finitely non-resonant spectral decompositions (162K, AMS-LaTex2e) Nov 11, 98

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Abstract. In this work we study $C^{k,s}, 2\leq k \leq \infty , 0\leq s \leq 1$, maps of a Banach space near a fixed point. We show the existance and uniqueness of a class of $C^{k,s}$ local invariant submanifolds of the stable manifold which correspond to a spectral subspace satisfying a finite non-resonance condition of order $L \leq k$ and an overriding condition of order $L\leq k$ (condition (3) of Theorem 1). We study the dependence of these invariant manifolds on a parameter that lies in a Banach space. We also show that a $C^{k,s}, 2\leq k \leq \infty , 0\leq s \leq 1$, local weak-stable manifold that satisfies these two conditions is unique.

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